Center of mass of two extended bodies

[aftershock]

Homework Statement

Consider a system comprising two extended bodies, which have masses M₁ and M₂ and centers of mass at R₁ and R₂. Prove that the CM of the whole system is at

[M₁R₁+M₂R₂] / [M₁+M₂ ]

Homework Equations

Definition of CM

The Attempt at a Solution

First I looked at the numerator of the equation given in the problem. If I replace R₁ with the definition then M₁ cancels. The same logic applies to the second term in the numerator. This leaves me with just the summation of all the mr terms for the particles comprising mass 1 and 2 then in the denominator I have the total mass of the system. So the equation given is now in the form of the definition? I feel like this is trivial, but the book has it marked as a harder problem. I feel like I'm missing something and it can't be done this easily. Is my method correct?

 

[voko]

The center of mass of a body is defined via an integral. The center of mass of two bodies is also defined via an integral, but this time integration is over two bodies. I think you are supposed to prove that the latter integral is indeed that sum.